SuPER Cart DC Motor Model

And

Ultra-Capacitor Addition

Joseph Witts

DC Motor Model DC Motor Testing In order to develop a model of the entire SuPER cart for simulation purposes, a model of the DC motor had to be developed. The first task was to contact the manufacture in order to obtain as much information about the motor as possible. A Dayton 6MK98 12V ¼ hp motor was purchased from Grainger. However, Dayton is not really a company but just a name that Grainger places on motors they sell. The real manufacture is Leeson, and the Leeson part number for the motor is 108949. The following parameters were obtained from Leeson. This information was obtained over the phone, because Leeson will not give written parameter values to the public. These values were used as a starting point for developing a model that matches the DC motor. Motor Resistance: 0.048Ω @ 25o C Back EMF Constant: 6.64 V/kRPM Motor Torque Constant: 0.56 lbs-in/A Rotational Inertia: 3.12 lb*in2

Armature Inductance: 0.33mH Stall Torque: 99 in-lbs @ 179A In order to properly model the DC motor, experimental data was required to determine how the motor reacted during start up conditions under load. So testing was conducted to determine how much current the DC motor was drawing during start up. This was tricky because there was no available equipment that could plot the current as a function of time. Since the test setup included only the battery and DC motor, the battery’s voltage drop during the start up of the motor was used to determine how much current the battery was supplying to the motor. This was accomplished by first determining the internal resistance of the battery, and then using the change in voltage of the battery to calculate the current supplied. The assumption that the battery’s internal resistance remains constant during motor start up was made, so the accuracy of the calculated data depends on how much the battery’s resistance changes. To determine the internal resistance of the battery the open circuit voltage of the battery was measured, and a shunt was placed in series with the motor to determine the current flowing in the circuit (Schematic 1).

DC Motor

Shunt

InternalResistance

BatteryBatteryTerminalVoltage

_

+

11.75 V

Schematic 1: Circuit used to determine the battery’s internal resistance

Next the motor was turned on with a 1.6 lbs-in load. The steady state battery terminal voltage and shunt voltage was measured and the battery’s internal resistance was calculated as follows. Open circuit battery voltage = Voc = 11.75 V Steady state battery terminal voltage = Vss = 10.50 V Shunt voltage = 15.5 mV

Shunt Ratio mVA

mVA 6.0

5030

==

Shunt current = ( ) AmVmVAI 3.95.156.0 =⎟

⎠⎞

⎜⎝⎛=

Battery’s Internal Resistance = Ω=−

=−

= 129.03.9

5.1075.11A

VVI

VssVocRBat

Now that the battery’s internal resistance is known. The current supplied by the battery can be calculated using the following formula:

BatRtVVoctI )()( −

=

Where V(t) values were taken from the oscilloscope trace of Plot 1. The voltage values and calculated current values during the motor’s starting in-rush can be seen in Data Table 1.

Plot 1: Battery terminal voltage trace with DC motor loaded at 8 in-lbs

Time (ms)

Voltage (V)

Current (A)

230 8.781 23.02 240 8.813 22.77 250 8.844 22.53 260 8.875 22.29 270 8.906 22.05 280 8.938 21.80 290 8.938 21.80 300 8.969 21.56 310 9.000 21.32 320 9.000 21.32 330 9.031 21.08 340 9.031 21.08 350 9.063 20.83 360 9.063 20.83 370 9.063 20.83 380 9.094 20.59 390 9.094 20.59 400 9.094 20.59 420 9.125 20.35 450 9.156 20.11 500 9.188 19.86 550 9.188 19.86 1000 9.188 19.86

Time (ms)

Voltage (V)

Current (A)

0 11.750 0.00 10 6.906 37.55 20 6.844 38.03 30 7.094 36.09 40 7.313 34.40 50 7.438 33.43 60 7.531 32.71 70 7.656 31.74 80 7.781 30.77 90 7.875 30.04 100 8.031 28.83 110 8.094 28.34 120 8.156 27.86 130 8.250 27.13 140 8.313 26.64 150 8.375 26.16 160 8.469 25.43 170 8.563 24.71 180 8.594 24.47 190 8.625 24.22 200 8.688 23.74 210 8.688 23.74 220 8.719 23.50

Data Table 1: Measured battery terminal voltage obtained from oscilloscope and calculated current DC Motor Modeling A PSpice model (Schematic 2) of a permanent magnet DC motor was found at http://www.ecircuitcenter.com/Circuits/dc_motor_model/DCmotor_model.htm where the author modeled the mechanical side of the motor with an electrical equivalent. Mechanical torque was represented by voltage, speed by current, and drag by a resistor.

Schematic 2: DC motor model found online After looking at the mechanical side of this model it became apparent that it can only be accurate for one value of torque. Schematic 3 is a simplified version of the mechanical side of the model. Once the motor reaches steady state operation the inertia can be ignored, so the speed is determined by torque and viscous drag (R). If the value of R is determined from the steady state values of Data Table 1, and the same value of R is used for rated torque the error is large as seen below.

R

Inertia

ViscousDragTorque

1 2

Schematic 3: Simplified mechanical side of the DC motor model Using measured values from Data Table 1 to calculate R: At steady state inertia does not need to be considered.

( )( DragViscousSpeedTorque _= )

kRPMinlb

kRPMinlb

SpeedTorqueR −

=−

== 944.7007.18

Using this value of R to calculate speed at rated torque:

( ) kRPMkRPM

inlbinlb

DragViscousTorqueSpeed 101.1

944.775.8

_=

−−

==

Error of the DC motor’s calculated speed using this value of R for rated speed:

%8.38%100800.1

800.1101.1−=×⎟

⎠⎞

⎜⎝⎛ −

=Error

So this model of a DC motor is missing some component that can yield more reliable results. I came across a document online for testing and modeling a DC motor at http://www.mech.utah.edu/~me3200/labs/motorchar.pdf that showed there was another component of drag that needs to be considered when modeling a motor. Coulomb drag, unlike viscous drag, is not a function of speed and is constant. So the coulomb drag was modeled as a DC voltage source opposing the applied torque voltage source of Schematic 4. To solve for the appropriate value of viscous and coulomb drag two equations with two unknowns needed to be developed. By using the steady state values in Data Table 1 and the motor’s rated values the two equations were developed. Below are the calculations used to determine the values of coulomb drag (X) and viscous drag (R) to be used in Schematic 4.

R

Inertia

ViscousDragTorque

Coulomb Drag

X

1 2

Schematic 4: Variables used to determine both viscous and coulomb drag At steady state inertia does not need to be considered.

( )(RSpeedXTorque += ) From measured values of Data Table 1

kRPMSpeedinlbTorque

007.18

=−=

)

Equation 1 ( ) ( )(RkRPMXinlb 007.18 +=−

DC motor’s rated values

kRPMSpeedinlbTorque

8.175.8

== −

Equation 2 ( ) ( )( )RkRPMXinlb 8.175.8 +=−

Equation 3, solving for X in Equation 2 ( ) ( RkRPMinlbX 8.175.8 −−= )( )

Substitute Equation 3 into Equation 1 ( ) ( ) ( )( ) ( )( )RkRPMRkRPMinlbinlb 007.18.175.88 +−−=−

( )kRPMinlb

kRPMinlbR −=

−= 9458.0

793.075.0

Substitute R into Equation 1 and solve for X

( ) ( ) ⎟⎠⎞

⎜⎝⎛ −

+=−kRPM

inlbkRPMXinlb 9458.0007.18

inlbX −= 048.7 Now that the values of viscous and coulomb drag have been determined, the rest of the DC motor’s model parameters can be found. The DC motor model has an electrical side and a mechanical side represented by electrical components. The electrical side uses an inductor to represent the motor’s armature inductance, a resistor for the armature resistance, and a current controlled voltage source to represent the back emf. The mechanical side uses a current controlled voltage source to represent the applied torque, a DC source for coulomb drag, an inductor for inertia, and a resistor for viscous drag. All of these parameters, except the two drags, where solved by trial and error by comparing the simulations output to the data gathered in Data Table 1. The manufactures supplied values were used for the initial motor parameters and adjusted until the simulated current waveform Plot 5 represented the actual current waveform Plot 4. See Schematic 5 for the final DC motor model circuit and parameters.

00

0

R_Motor0.16

Viscous_Drag0.9458

L_Motor0.7m

1

2

Inertia1.2

1

2

+-

TorqueKt=0.404

V_Battery11.75V

+-

Back_EMFKm=6.1

R_Battery

0.129

Coulomb_Drag7.048

Schematic 5: Final PSpice DC Motor Model Notice that the magnitude of the armature inductance and resistance is noticeably greater than the manufacturer’s values. This is because the testing setup measured the voltage across the battery’s terminals not the direct input to the motor. So the resistance and inductance of the wire going from the battery to the motor’s plug, and the 16 foot long cord for plugging in the motor, are added to the armatures inductance and resistance. To improve this model the voltage needs to be measured at the battery terminal and the input to the 16 foot long plug for the motor. This way the wire connecting the battery to the plug can be modeled separately, so the final motor model will represent only the motor and the 16 foot cord connected to the motor. The following plots below can be used to tell how well the model reflects the actual data by comparing the actual waveform of the current and voltage during the motor’s in-rush stage to the simulation. As you can see by comparing Plot 2 and Plot 3 the voltage sags are reasonably similar, and the current spike of Plot 4 and Plot 5 are also very similar. There is still room for improving the model by not lumping the impedance of the wire going from the battery to the plug and the 16 foot cord with the DC motor’s armature inductance and resistance. Since this is just the initial prototype phase of the project, and the wiring will likely change, further refinement of the model was not conducted. Plots 6 and 7 were included to show how the modeled DC motor’s applied torque and speed change as a function of time, and how the steady state values are very close to those in Data Table 1.

Battery Terminal Voltage During DC Motor In-Rush Mechanical Load = 8 in-lbs

6

7

8

9

10

11

12

0 100 200 300 400 500 600 700 800 900 1000

Time (ms)

Volta

ge (V

)

Plot 2: Plot of the actual battery terminal voltage from Data Table 1

Time

0s 0.1s 0.2s 0.3s 0.4s 0.5s 0.6s 0.7s 0.8s 0.9s 1.0sV(L_Motor:1)

6V

8V

10V

12V

Plot 3: Modeled DC motor’s battery terminal voltage

DC Motor In-Rush CurrentMechanical Load = 8 in-lbs

0

5

10

15

20

25

30

35

40

0 100 200 300 400 500 600 700 800 900 1000

Time (ms)

Cur

rent

(A)

Plot 4: Plot of the actual motor in-rush current from Data Table 1

Time

0s 0.1s 0.2s 0.3s 0.4s 0.5s 0.6s 0.7s 0.8s 0.9s 1.0sI(R_Battery)

0A

10A

20A

30A

40A

Plot 5: Modeled DC motor’s in-rush current draw

Time

0s 0.1s 0.2s 0.3s 0.4s 0.5s 0.6s 0.7s 0.8s 0.9s 1.0sV(Torque:3)

0V

4V

8V

12V

16V

Plot 6: Modeled DC motor’s torque in lb-in

Time

0s 0.1s 0.2s 0.3s 0.4s 0.5s 0.6s 0.7s 0.8s 0.9s 1.0sI(Coulomb_Drag)

0A

0.5A

1.0A

Plot 7: Modeled DC motor’s speed in kRPM Next the model was used to compare simulated values to actual data found on the wiki (files dc_motor and dc_motor_solar) and the motor’s rated values. As you can see from Data Table 2 the simulated values are reasonably close to the actual data. One discrepancy is with the dc_motor file simulation where the simulated speed is 12% less than the actual data. I’m not sure how the data was gathered for the dc_motor file, but if the recorded voltage is actually the motor voltage instead of the battery voltage this could account for the larger error. If this is true the simulation should have a slightly higher battery voltage, which will increase the simulated torque and speed slightly and decrease the error. As far as the 20.4% error for the motor operating at rated values, the error is likely due to the fact that the model has impedance of the wire going from the battery to the plug and the 16 foot cord, lumped together with the motor’s armature inductance and resistance. Even though the battery voltage is 14.45 V the actual voltage at the input of the motor (manufacture’s rated voltage location) is lower. So the real

percent difference is lower than 20%, due to the voltage drop across the wire going from the battery to the plug and 16 foot cord. Condition Battery Voltage (V) Torque (lb-in) Speed (rpm) Motor Current (A) Data Table 1 9.188 8.00 1007 19.86Simulation 9.188 7.98 988 19.76Percent Difference 0.0% -0.2% -1.9% -0.5%dc_motor_solar 12.2 8.00 1523 20.16Simulation 12.2 8.42 1453 20.85Percent Difference 0.0% 5.3% -4.6% 3.4%dc_motor 8.14 8.00 939 19.80Simulation 8.14 7.83 826 19.38Percent Difference 0.0% -2.1% -12.0% -2.1%Motor Rating 12 8.75 1800 21.00Simulation 14.45 8.75 1800 21.66Percent Difference 20.4% 0.0% 0.0% 3.1%

Data Table 2: Comparison of simulated and actual data Ultra-Capacitor In an attempt to extend the life of the battery the idea came about to use an ultra-capacitor for energy storage for short term high energy demands, like the in-rush current associated with starting the DC motor. Since the internal resistance of the battery and the battery’s open circuit voltage was known, a PSpice simulation was run to determine what would happen if the uncharged ultra-capacitor was placed across the battery (Schematic 6). It turns out that a large amount of current is drawn for a significant amount of time due to the large capacitance of the ultra-capacitor (Plot 8).

0

V_Battery12Vdc

R_Battery

0.129

ESR0.019

Ultra_Cap58

Schematic 6: Charging the ultra-capacitor without current limiting resistor

Time

0s 10s 20s 30s 40s 50s 60sI(R_Battery)

0A

50A

100A

Plot 8: High ultra-capacitor charging current due to lack of current limiting resistor To limit this charging current, a current limiting resistor needs to be added to the circuit. The parameters that were used to determine the appropriate resistor value were physical resistor size, power dissipation, and charging time. The larger the resistance, the smaller the resistors became because they had to dissipate less power, but this also increased the charging time. Likewise, the smaller the resistance, the larger the resistors become to dissipate a larger amount of power. To narrow down the options a total charging time of 15 minutes was determined to be an acceptable charging time, which equals five time constants. The required resistance value to yield this charging time was calculated as follows:

( )

( )( ) Ω=⎟⎠⎞

⎜⎝⎛

=⇒== 1.3585

minsec60min15

min1555F

RRCτ

Now that knowing a resistance of around 3Ω was needed to produce a charging time of 15 minutes, the power rating of the resistor could be calculated by using the nominal 12 volts of the battery.

( ) WVR

VP 483

12 22

=Ω

==

Using the calculated resistance and power rating, an Ohmite 270 series 3Ω 50W resistor was determined to be a good choice. Ideally the PV array should charge the ultra-capacitor instead of the battery. The problem with this is that the output of the DC-DC converter is usually between 13V and 14V. So the resistor needs to be able to handle the higher power dissipation due to the higher output voltage of the converter. The resistor’s datasheet states the resistor can take an overload of 10 times rated power for 5 seconds without damaging the resistor. A simulation was conducted using a 14V source simulating the DC-DC convert (Schematic 7), plotting the charging current and resistor power dissipation as a function of time (Plot 9). From the simulation one can conclude that the resistor can handle the increased power dissipation, since

the maximum power is only 1.3 times the rated value and decays to the rated value in about 20 seconds.

0

V_Conv erter14Vdc

ESR0.019

Ultra_Cap58

R_Charging

3

Schematic 7: Charging the ultra-capacitor with PV array using current limiting resistor

Time

0s 50s 100s 150s 200s 250s 300s 350s 400s 450s 500sW(R_Charging) I(R_Charging)

0

20

40

60

80

Plot 9: Charging current and power dissipated by the 3Ω current limiting resistor Operating Mode PCB Once the ultra-capacitor is charged to the same voltage as the battery, there is no need for the current limiting resistor. So a circuit needed to be developed that could switch a current limiting resistor in and out of the system. Since we are still in the prototype phase of the project we might have to remove the ultra-capacitor at some point, so there should be a provision to safely discharge the capacitor. So the circuit will have three different modes of operation called normal, charging, and discharging, and will be known as the operating mode PCB (Schematic 8). In normal mode power will come from the battery and pass through the board to the charged capacitor and the load bus (Schematic 9). During the charging mode a 3Ω resistor will be placed in series with the battery and capacitor to limit the initial charging current of the uncharged ultra-capacitor (Schematic 10). When in the discharge mode the ultra-capacitor will be isolated from the battery and connect to ground through a 3Ω resistor (Schematic 11). Power MOSFETs will be used to act as the switches on the operating mode PCB. The switching of the circuit will be controlled by the computer, so the board must be able to interface with the NiDAQ’s.

S2

S1Charging Resistor

DischargingResistor

Battery DC to DCConverter

0

To Load Bus

UltraCapacitor

S0

S3

Schematic 8: Simplified version of the operating mode PCB

S2

S1Charging Resistor

DischargingResistor

Battery DC to DCConverter

0

To Load Bus

UltraCapacitor

S0

S3

Schematic 9: Operating mode PCB in normal mode

S2

S1Charging Resistor

DischargingResistor

Battery DC to DCConverter

0

To Load Bus

UltraCapacitor

S0

S3

Schematic 10: Operating mode PCB in charging mode

S2

S1Charging Resistor

DischargingResistor

Battery DC to DCConverter

0

To Load Bus

UltraCapacitor

S0

S3

Schematic 11: Operating mode PCB in discharge mode The actual circuit is obviously more complicated than the simplified versions above, and was constructed on a six by eight inch board. Schematics 12 and 13 show the component connections on the PCB, while the rest of this section explains how components were selected.

C151u

R71k

BATTERY

MAIN LINE

GND

LOAD VOLTAGE

S0

S1

S2

U6LM2937ET-5.0

IN1 OUT 3

GN

D2

U5 LM2937ET-8.0

BATTERY IN1 OUT 3

GN

D2

Switch S3IRF2804

C80.1u

U7

MAX1822

C1+1

C1-7

C2+6

C2-2

Vcc

8G

ND

4

Vout 5

U8 SN7406N Inv eter

Input1

Input 3Output4Output

2

Input 5

Input 9

Input 11

Output6

Output8

Output10

Vcc

14G

ND

7

Input 13Output12

R451k

C910u

C101u

C111u

C121u

GND

Header f rom NiDAQ

1 2 3 4 5 6

C130.1u C14

10u

Schematic 12: First half of the operating mode PCB

ULTRA-CAPACITOR AND LOAD BUS

U2LM2937ET-3.3

IN1

OUT3

GN

D2

U1 LM2937ET-8.0

IN1 OUT 3

GN

D2

C161u

R81k

C171u

R91k

MAIN LINE

S2

Switch S2IRF2804

S1

C181u

S0

R101k

Switch S1IRF540

Switch S0IRF540

MAIN LINE

U3

MAX622

C1+1

C1-7

C2+6

C2-2

Vcc

8G

ND

4

Vout5

U4MM74C90X Buf f er

Output1

Output3

Input4

Input2

Output5

Output9

Output11

Input6

Input8

Input10

Vcc

14G

ND

7

Output13

Output12

R151k

R251k

R351k

C210u

C51u

C61u

C71u

C10.1u

C30.1u

GND

Charging3

Discharge3

LOAD VOLTAGE

R6

51k

R5

51k

C410u

U17

LM741

V+

7+

3OS2

5

OUT6

-2

V-

4

OS11

Schematic 13: Second half of the operating mode PCB

MOSFET Selection An IRF2804S power MOSFET was selected for switches S2 and S3, which are connected to the high current traces of the operating mode PCB. These MOSFET need to be rated for at least 30A continuous, with low on resistance to make the voltage drop across the MOSFETs as small as possible. The MOSFETs have a continuous drain current rating of 75A, and an on resistance of 2.5mΩ, so the voltage drop across each MOSFET will be 70mV at 30A. A D2pak package was used in order to increase the surface area that will carry the high current. The drain terminal on this package has a large flat surface that gets soldered directly to the board, which should also help to dissipate heat. The selection of switches S0 an S1 was not as critical as switches S2 and S3, since the will not have high current flowing through them. They also do not need a low on resistance, since they are only being used to charge and discharge the ultra-capacitor. An IRF540PBF power MOSFET rated for 28A and an on resistance of 77mΩ was selected. Since only a small amount of current will flow through these MOSFETs, a TO-220 was used to save board space. Gate Driver Selection Since the source terminal of the MOSFETs used for switches S1, S2, and S3 will be around 12 V when the switches are on, the gate voltage must be higher than 12V to turn the MOSFETs on. A Maxim MAX622 high-side power supply was selected to generate a gate voltage above 12V. The output voltage of the MAX622 is 11V higher than MAX622 supply voltage. Voltage Regulators The maximum gate to source voltage of the MOSFETs is 20V. If the MAX622 was supplied by the battery the output voltage would be the battery voltage plus 11V, which could be as high as 25V if the battery is being charged and the DC-DC converter is outputting 14V. This would cause the gate to source junction to breakdown if the source of the MOSFETs were ever grounded during a fault, or in the case of switch S0 connected to ground through the discharging resistor to discharge the ultra-capacitor. So an 8V regulator was selected for the MAX622’s Vcc to limit the voltage output to 19V. It turns out that even though the NiDAQ’s are supposed to output 5V for a high signal, they realistically can output as low as 2V according to Eran Tal’s thesis. So a 3.3V regulator was used for the buffer’s Vcc, to work with the NiDAQ’s low VOH. However the inverter has a 5V regulator for Vcc, which has a VIH minimum of 2V, so it is compatible with the NiDAQ’s. Buffer/Inverter Selection The control signals will comes out of the NiDAQs and to the inputs of either a buffer or inverter. A MM74C906 open drain buffer was used, so that when the input is high the output is floating.

And a SN7406 open collector inverter was used, so that when the input is low the output is floating. The outputs are connect to the MAX622’s output by a 51kΩ resistor. When the inverter or buffer’s output is low the MOSFETs are turned off, and when the outputs are floating the MOSFET’s gate voltage will be 19V turning them on. In an effort to make the PCB more reliable it needed to be determined if there are any conditions that could cause the NiDAQ’s to function strangely, and turn on a switch that should be off. It turns out there are two conditions. When the computer is initially turned on the NiDAQ’s output a high signal, which remains high until the program controlling the circuit switching is executed. If all the gates are driven by buffers connected to the NiDAQ, then all the MOSFETS turn on. Which means the battery will be connected to ground through a 3Ω resistor. So the idea of using inverters instead of a buffer to control the switching came up, but this yield a new problem. If the NiDAQs loose power their output is low, which will cause the inverters (powered by the battery) to output high turning all the switches on. So an extra switch (S3) was added to the board to eliminate the problem of turning on switches when they should be off. The board is set up so that the gate on switch S3 is connected to the NiDAQs through an inverter, and the control circuitry is powered directly by the battery. Whereas the gate on switch S0, S1, and S2 is connected to the NiDAQs through a buffer and the control circuitry is powered up only when switch S3 is on. This way when the NiDAQs are initially turned on and all outputs are high switch S3 is turned off, which de-energizes the control circuitry of switch S0, S1, and S2 turning them off. If the NiDAQs loose power and all outputs go low switch S0, S1, and S2 turn off, while switch S3 turns on. The best solution for this problem would be to purchase new NiDAQs that output low when initially energized, which means the board can function properly by only using buffers to interface with the NiDAQs. This way the cost and size of the board can be reduced by eliminating a number of components that will no longer be needed, such as switch S3 and all of its control circuitry. Operating Mode PCB Testing Once the operating mode PCB was constructed it needed to be tested before being installed on the SuPER cart. Since there are no power supplies that can supply 30A, the DC source from the AC machines lab was used. Data Table 3 shows voltage drop across switches S2 and S3 and the calculated MOSFET on resistance at different current values.

I (A) S2 (mV) S3 (mV) Rds on S3 (mΩ) Rds on S2 (mΩ) 5 13.3 8.3 1.7 2.7 10 22.6 19.1 1.9 2.3 15 32.5 25.0 1.7 2.2 20 49.5 41.2 2.1 2.5 22 53.7 45.9 2.1 2.4 25 59.6 50.6 2.0 2.4 28 66.7 55.9 2.0 2.4 30 72.4 59.9 2.0 2.4

Data Table 3: MOSFET on resistance of switch S2 and S3 Plot 10 shows the voltage drop across each as a function of current. The slope of the trend line represents the average on resistance, and this value could be used to describe the MOSFETs resistance for simulation purposes.

Voltage Drop Across MOSFETS

y = 2.4199x - 0.5978

y = 2.1147x - 2.7353

0

10

20

30

40

50

60

70

80

0 5 10 15 20 25 30 35

Current (A)

Volta

ge D

rop

(mV)

S3S2

Plot 10: Voltage drop across switch S2 and S3 DC Motor Model with Ultra-Capacitor Simulation Although there is no data to prove how well the simulation compares to actual results, the circuit (Schematic 14) was simulated to get an idea of how the circuit might behave when the DC motor is started with the ultra-capacitor connected. The in-rush DC motor current peaks at about 62A, with the battery suppling about 8A and the ultra-capacitor supplying about 54A. By looking at Plot 13 the DC motor’s torque reaches steady state in about 0.5 seconds. However, according to Plot 15 the speed doesn’t reach steady state until 35 seconds after start up which seems rather long. If the circuit does behave like the simulation, then the battery is definitely not suppling a large amount of current during motor start up. The bulk of the current is coming from the ultra-capacitor.

00

0

R_Motor0.16

Viscous_Drag0.9458

L_Motor0.7m

1

2

Inertia1.2

1

2

+-

TorqueKt=0.404

V_Battery11.75

+-

Back_EMFKm=6.1

ESR0.019

Ultra-Cap58

R_Battery

0.129

Coulomb_Drag7.048

Schematic 14: DC motor simulation with ultra-capacitor

Time

0s 5s 10s 15s 20s 25s 30s 35s 40s 45s 50s 55s 60sI(R_Battery) I(ESR) I(L_Motor) V(Ultra-Cap:+)

0

20

40

60

80

Plot 11: Ultra-capacitor voltage and battery, ultra-capacitor, and DC motor current at steady state

Time

0s 0.1s 0.2s 0.3s 0.4s 0.5s 0.6s 0.7s 0.8s 0.9s 1.0sI(R_Battery) I(ESR) I(L_Motor)

0A

20A

40A

60A

80A

Plot 12: Battery, ultra-capacitor, and DC motor current during in-rush

Time

0s 0.1s 0.2s 0.3s 0.4s 0.5s 0.6s 0.7s 0.8s 0.9s 1.0sV(Torque:3)

0V

10V

20V

30V

Plot 13: Modeled DC motor’s torque in lb-in with ultra-capacitor

Time

0s 0.1s 0.2s 0.3s 0.4s 0.5s 0.6s 0.7s 0.8s 0.9s 1.0sI(Coulomb_Drag)

0A

0.5A

1.0A

1.5A

Plot 14: Modeled DC motor’s peak speed in kRPM with ultra-capacitor

Time

0s 10s 20s 30s 40s 50s 60sI(Coulomb_Drag)

0A

0.5A

1.0A

1.5A

Plot 15: Modeled DC motor’s steady state speed in kRPM with ultra-capacitor

Parts List Description Part # Newark Part # Price R1 51kΩ MCRC1/4G513JT-RH 73K0336 0.128R2 51kΩ MCRC1/4G513JT-RH 73K0336 0.128R3 51kΩ MCRC1/4G513JT-RH 73K0336 0.128R4 51kΩ MCRC1/4G513JT-RH 73K0336 0.128R5 51kΩ MCRC1/4G513JT-RH 73K0336 0.128R6 51kΩ MCRC1/4G513JT-RH 73K0336 0.128R7 1kΩ MCRC1/4G102JT-RH 72K6178 0.128R8 1kΩ MCRC1/4G102JT-RH 72K6178 0.128R9 1kΩ MCRC1/4G102JT-RH 72K6178 0.128R10 1kΩ MCRC1/4G102JT-RH 72K6178 0.128 Total 1.28

Description Part # Newark Part # Price C1 0.1μF KME50VBR10M5X11LL 91F3293 0.143C2 10 μF 106CKH100M 69K7898 0.106C3 0.1 μF KME50VBR10M5X11LL 91F3293 0.143C4 10 μF 106CKH100M 69K7898 0.106C5 1 μF 105CKH050M 69K7895 0.038C6 1 μF 105CKH050M 69K7895 0.038C7 1 μF 105CKH050M 69K7895 0.038C8 0.1 μF KME50VBR10M5X11LL 91F3293 0.143C9 10 μF 106CKH100M 69K7898 0.106C10 1 μF 105CKH050M 69K7895 0.038C11 1 μF 105CKH050M 69K7895 0.038C12 1 μF 105CKH050M 69K7895 0.038C13 0.1 μF KME50VBR10M5X11LL 91F3293 0.143C14 10 μF 106CKH100M 69K7898 0.106C15 1 μF 105CKH050M 69K7895 0.038C16 1 μF 105CKH050M 69K7895 0.038C17 1 μF 105CKH050M 69K7895 0.038C18 1 μF 105CKH050M 69K7895 0.038 Total 1.38

Description Part # Mouser Part # Price X1 15 amp terminal 7690 534-7690 0.46X2 15 amp terminal 7690 534-7690 0.46X3 15 amp terminal 7690 534-7690 0.46X4 15 amp terminal 7690 534-7690 0.46X5 30 amp terminal 8196 534-8196 1.24X6 30 amp terminal 8196 534-8196 1.24X7 30 amp terminal 8196 534-8196 1.24 Total 5.56

Description Part # Newark Part # Price U1 8V Regulator LM2937ET-8.0 07B6337 2.62 U2 3.3V Regulator LM2937ET-3.3 41K4552 2.49 U3 High-Side Power Supply MAX622 0 U4 Buffer MM74C906N 58K1928 2.58 U5 8V Regulator LM2937ET-8.0 07B6337 2.62 U6 5V Regulator LM2937ET-5.0 41K4553 2.62 U7 High-Side Power Supply MAX1822 0 U8 Inverter SN7406N 08F7825 1.05 U9 MOSFET IRF540PBF 63J7322 1.00 U10 MOSFET IRF540PBF 63J7322 1.00 U15 MOSFET IRF2804SPBF 73K8240 3.55 U16 MOSFET IRF2804SPBF 73K8240 3.55 U17 Op Amp LM741 78K6012 0.296 Total 23.38

Description Part # Newark Part # Mouser Part # Quantity Price Total 3 ohm 50W L50J3R0E 64K5014 2 8.61 17.22Crimp Connector 3-350980-1 52K4327 6 0.061 0.3666 terminal housing 640250-6 571-6402506 1 0.17 0.176 terminal header 640445-6 571-6404456 1 0.18 0.18 Total 17.94

How to Operate the SuPER Cart

SuPER Prototype Operation Modified 6/11/07 J. Witts

1) Ensure that all breakers are open. 2) Insert the hub cables into the laptop USB ports, followed by the NI DAQ device cables.

Then insert the PIC cable into the open laptop port. The mouse cable should be inserted into the hub.

3) Power on the laptop (at this point running on its internal battery) and at the GRUB window choose the latest version of Red Hat.

4) Login using root:super1. 5) Open a shell and change directories (cd) to /home/super1/pvpro/src to control the PV

and main switch board. 6) Close PV, converter and battery circuits by flipping the breakers marked PV, BATT

and BUS. The PV array will start charging the battery even though no programs are running, because the NiDAQ’s default output is high (turning MOSFET switches on).

7) Execute the software with the command ./contAcquireNChan . 8) Open a new shell and change directories (cd) to /home/super1/cap/src to control the

ultra-capacitor board. 9) Execute the software with the command ./cap .

10) If the ultra-capacitor is not needed leave the breaker labeled CAP open, enter n to operate the capacitor board in normal operation, and skip to step 14. If the capacitor is needed proceed to step 11.

11) Check the capacitor voltage with a voltmeter. If the capacitor voltage is within 2 V of the battery terminal voltage, run the capacitor board in normal mode. If the capacitor voltage is not, run the capacitor board in charging mode. Once the capacitor voltage is within 2 V of the battery terminal voltage, change the operating mode from charging to normal. Follow prompt and enter correct mode of operation.

‘c’ to charge the capacitor (used if capacitor is not at battery voltage) ‘n’ for normal operation (used to operate the cart without any resistors)

12) Once the capacitor board is operating in the correct mode determined from step 11, close the breaker labeled CAP. Once the capacitor is at the same voltage as the battery node and the operating mode is set to normal, the SuPER cart is ready to operate

13) Close the breakers as desired to power indicated loads. 14) To turn the system off, open all circuit breakers connected to the load bus. 15) While in the shell for the ultra-capacitor board type ‘o’ to turn all switches off (used to turn all capacitor board switches off) then

‘q’ to quit (used to exit program) 16) Now go to the shell running the PV software and use ‘q’ to quit. 17) Shut everything down by opening all circuits at the breakers.

Note: If the ultra-capacitor has to be physically taken off the cart it must be discharged first.

Follow the instructions below to safely disconnect the ultra-capacitor. 1) Follow steps 1 through 4 listed above. 2) Close the breaker labeled BATT. 3) Follow steps 8 through 9 to run the ultra-capacitor board software. Set the board to run in

discharge mode by entering d. 4) Close the breaker labeled CAP. 5) When capacitor is fully discharged (use voltmeter to ensure 0 V) turn off the system

following step 15 listed above. The capacitor can now be safely removed. Circuit Breaker Rearrangement In order to connect the capacitor to the SuPER cart, some of the circuit breakers needed to be moved. The 2 amp circuit breaker labeled BUS, that powers the sensors and control elements, had to be removed from the load bus. When the ultra-capacitor is charging it pulls the bus voltage down to zero volts, then slowly rises to the battery’s voltage. When the voltage is pulled down to zero, none of the control circuitry can be used. This means the PV array cannot be used to charge the ultra-capacitor, only the battery will be able to charge the ultra-capacitor. So by moving the BUS circuit breaker off the load bus and powering it off the battery, the PV array can now be used to charge the ultra-capacitor.

A 6 amp circuit breaker was selected to protect the capacitor. The breaker size was selected based on looking at the simulated capacitor current during start up (plot 12), and compared to the circuit breaker curve of plot 16. Since the circuit breaker curve is based on constant current during a fault, the breaker should not operate for the decaying transient of the DC motor’s in-rush current. The ultra-capacitors circuit breaker could not be directly connected to the load bus, since the circuit breakers can only interrupt faults in one direction. The construction of the circuit breaker only allows mounting in one direction, so it had to be installed adjacent to the load bus. See Schematic 15 for actual breaker locations. The circuit breaker was connected this way to interrupt fault current supplied by the ultra-capacitor if the load bus, or any point connected to the load bus, was faulted to ground.

Plot 16: CBI circuit breaker curve

Schematic 15: Gavin Baskin’s SuPER schematic